However, for many models of interest, there is no straightforward way to write down the likelihood function associated with the model. This is often due to the intractability of deriving a closed form expression for the model likelihood. In such situations, it may nevertheless be possible to apply a simulation-based inference approach termed Approximate Bayesian Computation [1]}, that substitutes a kernel on some statistics of the data for the model likelihood, and evaluates the fit of the model at a given set of parameter values through simulations. For given parameter realisations, the model is simulated, and the statistics of the simulated data compared with the same statistics of the observed data. Informally, regions of parameter space that correspond to simulated data sets whose statistics are “more similar" to those of the observed data will be associated with higher posterior probability than regions corresponding to simulated data sets with statistics that are “less similar" (where “similarity" is quantified using a pre-specified distance function).
